As I was told – in contrast to the English variant – the only initial empty hole is not located in the center of the board but has to be placed at a slightly different position in order to be able to solve the game (as I found later, the solver was not able to solve the game for an initially empty hole in the center of the board). Efficiently Solving the Diamond-41 BoardĪs the name suggests, the Diamond-41 board consists of 41 holes. This stirred my interest in the game again and I spent several hours writing a solver using bit boards and some other enhancements for this board, as described in the following section. Recently, I again stumbled across peg solitaire when I saw a different board with the shape of a diamond. The solver gave me the following solution: With a slightly adjusted move ordering the solver apparently needs much more time (several hours). I suppose that I was actually quite lucky with the standard move ordering that I was using. It is not nice nor efficient, but surprisingly finds the solution in less than a second.
The code is attached at the end of this post. Since I could never solve the game myself I decided to write a solver for the problem. When I started programming a few years ago, English peg solitaire was one of my first projects. The solution for the diamond shaped board is even more tricky. Many players need quite a few attempts in order to find the solution for the English peg solitaire. The English variant is shown in the figure below.Įven though the rules of the game are rather simple, finding a solution is not trivial. The English variant, as shown below, has one additional rule: In order to win, it is not sufficient that only one peg is left in the end this peg also has to be located in the center of the board. This is the case when there is no pair of pegs which are orthogonally adjacent or if only one peg is left. Once no move is possible any longer, the game is over. So, in each move, one peg jumps 2 holes further and the peg in-between is removed. The neighboring peg is then removed, leaving an empty hole. In each move the player selects one peg and jumps – either vertically or horizontally, not diagonally – with this peg over a directly neighboring one into an empty hole. For example, the English variant consists of 33 holes while the typical diamond variant consists of 41 holes. The number of holes depends on the board variant. Peg solitaire is a one-player game played on a board with holes and pegs. Many of us might now the board game peg solitaire and might even have one of its many variants at home. Marketed version of these games often give ranks to players depending on how many pegs they have left on the board.Solving Peg Solitaire with efficient Bit-Board Representations The complement problem, which is not attainable on all boards, is where one begins with a single hole vacant and ends the game with only one peg left in that initially vacant hole. In other variations, players may attempt to form some pattern of pegs at the end of the game. In variations, a player may start with some pattern on the board (several holes vacant) and then attempt to reduce to just one. The objectives vary but the most common is to start with a single hole vacant on the board and end up with a single counter (peg) at the end of the game. The French, however, did bring solitaire into popularity and the game retains its French name. This story, however, is only an inaccurate legend and it turns out that solitaire had already been around for quite some time. The game or, more accurately, puzzle of solitaire is oft reported to be invented by a French nobleman while imprisoned during the Revolution at the end of the eighteenth century. Elaborate maritime Solitaire board from the House on the Rock in Spring Green, Wisconsin, USA.
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